All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Islamic law deems it forbidden for a woman to ask her husband to divorce her without a Sharee‘ah-acceptable excuse. The Messenger of Allah, sallallaahu ‘alayhi wa sallam, said: “Any woman who asks her husband to divorce her for no (valid) reason, the scent of Paradise is forbidden to her.” [At-Tirmithi and others]
According to the Islamic law, a husband’s marriage to another wife is not a valid reason for requesting a divorce. If her husband refuses to divorce her, he is not denying her any of her rights by doing so. When a man takes one wife or more, he is only doing what he is allowed to do by the Sharee‘ah, which also stipulates the condition of treating all his wives fairly and establishing justice among them.
Divorce incurs grave harms, as it destroys the family and deprives the children of a normal upbringing under the care of both parents, and it also incurs psychological and social harms on the divorced woman that are much graver than the harms of living with her husband who has another wife. A woman might be driven by her emotions to ask for divorce and then regret it. The harms incurred by divorce are incomparable to the pain of coexisting with a co-wife.
We would like to point out that there is no religious impediment to attempting to reach an understanding with the husband and seeking the help of some wise relatives or other people to try to dissuade him from his decision to take a second wife, if there is no real need for a second marriage. If your husband insists on taking another wife or needs to take another wife, then you should fear Allah, adhere to patience, and live with him in kindness.
Allah Knows best.